✦ LIBER ✦

Characterizations of the polynomial numerical hull of degree k

✍ Scribed by James V. Burke; Anne Greenbaum

Publisher: Elsevier Science
Year: 2006
Tongue: English
Weight: 158 KB
Volume: 419
Category: Article
ISSN: 0024-3795
DOI: 10.1016/j.laa.2006.04.023

No coin nor oath required. For personal study only.

✦ Synopsis

Six characterizations of the polynomial numerical hull of degree k are established for bounded linear operators on a Hilbert space. It is shown how these characterizations provide a natural distinction between interior and boundary points. One of the characterizations is used to prove that the polynomial numerical hull of any fixed degree k for a Toeplitz matrix whose symbol is piecewise continuous approaches all or most of that of the infinite-dimensional Toeplitz operator, as the matrix size goes to infinity.

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